If there were any doubts about what would be the first major challenge for this new coalition government, they were answered this past week: university funding. Vince Cable lit the blue touch paper (in the Observer) with the suggestion that the number of university places could be cut. Then, in a far-sighted speech, the universities minister, David Willetts, talked about the cost of subsidising degrees and the pressure on the taxpayer which was widely interpreted as an acknowledgement that tuition fees would have to rise. The new deputy leader of the Liberal Democrats, Simon Hughes, responded promptly to remind us that his party still opposes tuition fees.

The real concern for us now is that, if disagreements arise, our world-class university system faces the real possibility of a funding "valley of death". At exactly the same time as virtually all our international competitors have invested heavily in universities, the Labour government announced cuts (in England) of £449m to the planned higher education funding council budget for 2010-11, with a further £600m to be found from the higher education and science budgets by 2013. The new government added £200m of further cuts last month out of a higher education and science spend of around £14bn. But the truly scary prospect is what lies ahead.

Imagine the cross-section of a valley: universities stand on the top left of the valley and look down into the abyss as impending government funding cuts take spending well below current levels; on the other side of the valley there is the prospect of increased funding introduced by the review into university financing, including tuition fees, that began earlier this year, chaired by Lord Browne, the former chief executive of BP. .

But there are five worries about the shape of this valley. First, how steep will the gradient be as we go down the side as government cuts reduce spending, and over how long a time period?

The Institute of Fiscal Studies (IFS) posited before the election that, whoever won, further reductions in unprotected government departments in the order of 20%-25% by 2015 compared with the March 2010 budget would be required to restore public finances. We must await the 22 June budget to get confirmation of the overall picture of government finances, and for the October comprehensive spending review for individual departmental details, but these figures imply three or four years of reductions in addition to those already announced. Front-loading any cuts to universities over the next few years would be a truly disastrous scenario for the sector.

Second, how far down will universities have to go to reach the floor of the valley? If we simply assume that universities fare equally badly (or well) as all other areas, the IFS calculations imply an overall reduction of around 20%-25%, which could total about £3.5bn off the £14bn currently spent on higher education and science. I do not think that any government would inflict that damage on what all external analysis confirms is one of the UK's major routes to future societal and economic success, but that is what the IFS analysis implies.

Third, how steep will be the gradient as we come up the other side of the valley and, crucially, how far back up the valley will that funding take university spending? It would be very disappointing if Lord Browne's recommendations simply substituted lost government expenditure. There must be additionality, which is essential to match the increased expenditure that competitor nations are investing in their university systems.

Fourth, is there not a danger that Lord Browne's review, by opening up the prospect of "solving" the funding problems of universities, might allow politicians to cut more deeply than might be undertaken otherwise, only to find that Lord Browne's recommendations are not palatable to all members of the coalition? In short, might the Treasury see in Lord Browne's review a reason for inflicting higher cuts on universities because there is a source of substitute funds? And, as a double whammy, might these substitute sources fail to materialise as Parliament proves unwilling to pass his recommendations? That would be a national catastrophe.

Fifth, whatever the answers to the previous questions, there is the issue of how we get across the valley: we need a bridge. What looks certain is that there will be a number of years when government funding will fall and before Lord Browne's recommendations can be fully implemented. Put simply, public finances face about four years of cuts and possibly as long as eight years.

Equally, even if Lord Browne reports ahead of schedule, this summer, his recommendations can only be implemented as each cohort of new students starts, beginning in 2013 or 2012 at a push; thus it will be 2014/15 at the very earliest before any increase in the private contribution reaches a steady state.

Therefore, even if Lord Browne comes up with a way of replacing all lost government funding (as well as providing additional investment), and even if Parliament approves of his recommendations, there are at best five years before we get back to the same funding levels as exist now. This poses three massive challenges: first, we have to protect the quality of the student experience during that period and that cannot be done easily if the reductions are significant. Universities can, and must, make efficiency savings, but reductions of the kind implied by IFS calculations could not happen without affecting the student experience.

Second, we have already seen significant staffing losses in universities as financial pressures force institutions to reduce expenditure. The sector makes a surplus of only about 2%, and if cuts on the scale implied by the IFS occur, there will be significantly more instability in the finances of universities. Third, it is vital for the future of the UK as a leading knowledge-economy that spending on science and research are protected: other countries are pumping money into these areas because they are the key to future economic prosperity.

From every single conversation I have had with past or current ministers, every one of them values universities and sees them as essential for the future social and economic prosperity of the UK. Now is the time to build the bridge over the valley of death: we must all have the vision and the courage to make sure that we do not sleep-walk into the abyss.

Professor Steve Smith is president of Universities UK (and vice-chancellor, University of Exeter)